There are a number of different HDMI standards and connectors that are available, but broadly speaking they fall into three groups:
HDMI 1.2 - This is the first version of HDMI that become popular, and at the time of writing it is still the most common. It has a maximum speed of 165 Mpixel/s video (1080 pixels at 60 Hz, or UXGA) and 8-channel/192 kHz/24-bit audio. It uses connectors known as 'Type A', which are 13.9 mm wide by 4.45 mm high.
HDMI 1.3 with Type A connector. This is a later specification of HDMI using exactly the same connectors as HDMI 1.2, but requires higher specification cables. HDMI 1.3 is over twice the speed of HDMI 1.2 at a bandwidth of 340 MHz (10.2 Gbit/s). As the connectors are the same as HDMI 1.2, this cable may also be used for a HDMI 1.2 connection.
HDMI 1.3 with Type C connector. Also known as a 'Mini HDMI' connector, this new connector was made available for HDMI 1.3, which is smaller than the Type A connector at 10.42 mm wide by 2.42 mm high. This new connector was designed with camcorders in mind, but will naturally see more widespread use.
Check the manuals for the equipment that you wish to connect, and they will let you know which of these three types of cable you require.